caristi s fixed point theorem and selections of set valued contractions we show without the axiom of choice that the zermelo theorem implies directly a restriction of the caristi fixed point theorem to continuous functions under the axiom of choice this restriction is proved to be equivalent to caristi s theorem we also discuss kirk s problem on an extension of the caristi theorem and we establish two selection theorems for set valued contractions

a rapidly convergent iteration method and gâteaux differentiable operators abstract let fr 0 r p be a family of banach spaces satisfying if 0 r1 r2 p i fr1 fr2 ii f r1 f r2 f f r1 and iii r ln f r is a convex function let g0 be a banach space and f be a g teaux differentiate mapping and suppose that f x fp is dense in g0 under appropriate assumptions the equation f x 0 has a solution in fr for 0 r p the results extend the inverse function theorem of j moser to the class of g teaux differentiable operators

coupled fixed point theorems for multi valued nonlinear contraction mappings in partially ordered metric spaces abstract in this paper we establish two coupled fixed point theorems for multi valued nonlinear contraction mappings in partially ordered metric spaces the theorems presented extend some results due to ciric 2009 3 an example is given to illustrate the usability of our results

some common fixed point theorems for mappings and multi valued mappings using certain weak conditions of commutativity we prove some common fixed point theorems in complete metrically convex spaces which in turn generalize results due to assad and kirk itoh khan and several others

function variational principles and coercivity abstract the function type extension of ekeland s variational principle j math anal appl 47 1974 324 353 due to zhong nonlinear anal 29 1997 1421 1431 is deductible in a simplified manner and in a larger functional context this is also true for his normed coercivity result based on palais smale techniques

mizoguchi takahashi s fixed point theorem is a real generalization of nadler s abstract we give an example which says that mizoguchi takahashi s fixed point theorem for set valued mappings is a real generalization of nadler s we also give a very simple proof of mizoguchi takahashi s theorem

coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces abstract we introduce the concept of a mixed g monotone mapping and prove coupled coincidence and coupled common fixed point theorems for such nonlinear contractive mappings in partially ordered complete metric spaces presented theorems are generalizations of the recent fixed point theorems due to bhaskar and lakshmikantham t g bhaskar v lakshmikantham fixed point theorems in partially ordered metric spaces and applications nonlinear anal tma 65 2006 1379 1393 and include several recent developments

fixed point theorems for set valued contractions in complete metric spaces abstract the fixed point theory of set valued contractions which was initiated by nadler s b nadler jr multi valued contraction mappings pacific j math 30 1969 475 488 was developed in different directions by many authors in particular by s reich fixed points of contractive functions boll unione mat ital 5 1972 26 42 n mizoguchi w takahashi fixed point theorems for multivalued mappings on complete metric spaces j math anal appl 141 1989 177 188 y feng s liu fixed point theorems for multi valued contractive mappings and multi valued caristi type mappings j math anal appl 317 2006 103 112 in the present paper the concept of contraction for set valued maps in metric spaces is introduced and the conditions guaranteeing the existence of a fixed point for such a contraction are established one of our results essentially generalizes the nadler and feng liu theorems and is different from the mizoguchi takahashi result the second result is different from the reich and mizoguchi takahashi results the method used in the proofs of our results is inspired by mizoguchi takahashi and feng liu s ideas comparisons and examples are given

on the ray walker extension of the caristi kirk fixed point theorem on demontre que le theoreme de ray walker pour des operateurs non lineaires sur des espaces de banach est equivalent au theoreme de caristi kirk

some new fixed point theorems of generalized nonlinear contractive multivalued maps in complete metric spaces in this paper we present some new fixed point theorems for generalized nonlinear contractive multivalued maps and these results generalize or improve the corresponding recent fixed point results in the literature

abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity critical point theorems and applications to some nonlinear problems with strong resonance at infinity p bartolo and v benci istituto di matematica applicata via re david x0 bari ital and istituto di analisi matematica palazzo ateneo l ia scolai 2 bari italy received in revised form 20 december 1952

a concept of the mass center of a system of material points in the constant curvature spaces this article demonstrates that in the lobatchevsky space and on a sphere of arbitrary dimensions the concept of the mass center of a system of mass points can be correctly defined presented are a uniform geometric construction for defining the mass center hyperbolic and spheric lever rules the theorem of uniqueness for determining the mass center in these spaces among the compact manifolds only the sphere possesses this property

mapping theorems for gateaux differentiable and accretive operators let p be a nonlinear operator mapping the banach space x into the banach space y there are many approaches to studying solvability of the equation px y for y e y a considerable number of which involve local or infinitesimal assumptions on the operator p this is due in part to the fact that p frequently arises from a differential or integral operator which has monotonicity or smoothness properties for which local apriori estimates are readily obtainable in this paper we derive mapping theorems for operators p satisfying two different kinds of local assumptions differentiability assumptions and monotonicity assumptions our approach in the former case relies on an abstract newton kantorovich scheme which was pioneered by m altman see for example l and further developed in 19 in the latter case we extend some results of f e browder using a combination of both new and standard techniques in each case our basic technique involves an application of a new version of ekeland s theorem which we derive from a fundamental maximal principle of h brezis and f e browder in section 2 of this paper we derive our new version of ekeland s theorem and in section 3 apply this result to nonlinear operators using different and by now standard techniques we prove a domain invariance result in section 4 needed for our result an accretive operators

the palais smale condition versus coercivity possesses a convergent subsequence and cp is said to satisfy ps if ir satisfies ps for every c e ir recently among other results in critical point theory shujie i i showed that if a c functional p x k is bounded from below and satisfies the condition ps then p is coercive shujie s proof uses a gradient flow approach through the so called deformation theorem cf 3 io and for that he needs the notion of a pseudo gradient vector field tjassociated with the functional cp whose existence is guaranteed for c functionals by palais 8 in this paper we present some new results which relate the palais smale condition and the notion of coercivity and are based on the well known variational principle due to ekeland 5 61 in particular a new proof of the above mentioned result of shujie is given it should be pointed out that throughout the paper the given functional p could be assumed to be only gateaux differentiable rather than c and in addition to being conceptually simpler this approach could be used in more general situations where the functional is not even differentiable cf 4 the strong form of ekeland s variational principle to be repeatedly used is given in the following theorem

existence and uniqueness of common fixed points for two multivalued operators in ordered metric spaces in this paper we discuss some new fixed point theorems for a pair of multivalued operators which satisfy weakly generalized contractive conditions our results are the extension and improvement of corresponding results of j harjani and k sadarangani fixed point theorems for weakly contractive mappings in partially ordered sets nonlinear analysis 71 2009 3403 3410 and x zhang common fixed point theorems for some new generalized contractive type mappings j math anal appl 333 2007 780 786 finally some examples are given to illustrate the usability of our results

the n steps invasion percolation model abstract a new kind of invasion percolation is introduced in order to take into account the inertia of the invader fluid the inertia strength is controlled by the number n of pores or steps invaded after the perimeter rupture the new model belongs to a different class of universality with the fractal dimensions of the percolating clusters depending on n a blocking phenomenon takes place in two dimensions it imposes an upper bound value on n for pore sizes larger than the critical threshold the acceptance profile exhibits a permanent tail

common fixed point results for two new classes of hybrid pairs in symmetric spaces abstract some common fixed point theorems due to abbas and khan m abbas a r khan common fixed points of generalized contractive hybrid pairs in symmetric spaces fixed point theor appl 2009 2009 11 article id 869407 doi 10 1155 2009 869407 and abbas and rhoades m abbas b e rhoades common fixed point theorems for hybrid pairs of occasionally weakly compatible mappings defined on symmetric spaces pan amer math j 18 1 2008 55 62 are proved for two new classes of hybrid pair of mappings which contain occasionally weakly compatible hybrid pairs as a proper subclass consequently some results proved by hussain et al n hussain m a khamsi a latif common fixed points for jh operators and occasionally weakly biased pairs under relaxed conditions nonlinear anal 74 2011 2133 2140 bhatt et al a bhatt et al common fixed point theorems for occasionally weakly compatible mappings under relaxed conditions nonlinear anal 73 2010 176 182 and many others are extended to hybrid pair of mappings examples are also presented to support the concepts defined in the paper

l estimates for the bar partial problem in a half planeproblem in a half plane l approche de dualite pour trouver des solutions de f est suffisante pour plusieurs problemes apparaissant en theorie h p on donne des operateurs solution qui permettent de resoudre des problemes non resolubles par la dualite

fixed points of generalized contractive multi valued mappings in a recent paper n mizoguchi and w takahashi gave a positive answer to the conjecture of s reich concerning the existence of fixed points of multi valued mappings that satisfy a certain contractive condition in this paper we provide an alternative and somewhat more straightforward proof for the theorem of mizoguchi and takahashi also the problems associated with fixed points of weakly contractive multi valued mappings are studied finally we make a few comments that improve other results from their paper j math anal appl 141 1989 177 188

some common fixed point theorems for weakly compatible mappings abstract jungck s g jungck compatible mappings and common fixed points int j math math sci 9 1986 771 779 notion of compatible mappings is further extended and used to prove some common fixed point theorems for weakly compatible non self mappings in complete convex metric spaces we improve on the method of proof used by rhoades b e rhoades a fixed point theorem for non self set valued mappings int j math math sci 20 1997 9 12 and ahmed and rhoades a ahmed b e rhoades some common fixed point theorems for compatible mappings indian j pure appl math 32 2001 1247 1254 and obtain generalization of some known results in particular a theorem by rhoades b e rhoades a fixed point theorem for non self set valued mappings int j math math sci 20 1997 9 12 is generalized and improved

multi valued nonlinear contraction mappings abstract two concepts of nonlinear contractions for multi valued mappings in complete metric spaces are introduced and three fixed point theorems are proved presented theorems are generalizations of very recent fixed point theorems due to klim and wardowski d klim d wardowski fixed point theorems for set valued contractions in complete metric spaces j math anal appl 334 2007 132 139 and feng and liu y feng s liu fixed point theorems for multi valued contractive mappings and multi valued caristi type mappings j math anal appl 317 2006 103 112 as well as a fixed point theorem of mizoguchi and takahashi n mizoguchi w takahash fixed point theorems for multi valued mappings on complete metric spaces j math anal appl 141 1989 177 188 and several others an example is given to show that presented results are genuine generalizations our results are also some contribution to an open problem raised by reich s reich fixed points of contractive functions boll unione mat ital 5 1972 26 42 s reich some fixed point problems atti acad naz lincei 57 1974 194 198 s reich some problems and results in fixed point theory contemp math 21 1983 179 187

fixed point results for set valued contractions by altering distances in complete metric spaces nadler s contraction principle has led to fixed point theory of set valued contraction in non linear analysis inspired by the results of nadler the fixed point theory of set valued contraction has been further developed in different directions by many authors in particular by reich mizoguchi takahashi feng liu and many others in the present paper the concept of generalized contractions for set valued maps in metric spaces is introduced and the existence of fixed point for such a contraction are guaranteed by certain conditions our first result extends and generalizes the nadler feng liu and klim wardowski theorems and the second result is different from the reich and mizoguchi takahashi results as a consequence we derive some results related to fixed point of set valued maps satisfying certain conditions of integral type

solving the banach fixed point principle for nonlinear contractions in probabilistic metric spaces abstract the probabilistic version of the classical banach contraction principle was proved in 1972 by sehgal and bharucha reid v m sehgal a t bharucha reid fixed points of contraction mappings on pm spaces math syst theory 6 97 102 their fixed point theorem is further generalized by many authors in the intervening years many others have proved the probabilistic versions of the other known metric fixed point theorems however the problem to prove the probabilistic versions of the very important generalization of the banach contraction principle obtained in 1969 by boyd and wong d w boyd j s w wong on nonlinear contractions proc am math soc 20 1969 458 464 who proved the fixed point theorem for a self mapping of a metric space satisfying the very general nonlinear contractive condition is unsolved in these days similarly as in the metric space case to prove a fixed point theorem for a mapping satisfying the general probabilistic nonlinear contractive condition it was necessary to find a new approach substantially different from the previous technique for cases where a mapping satisfies the probabilistic linear contraction condition introduced by sehgal and bharucha reid and further used by many authors so the problem to obtain a truthful probabilistic version of the banach fixed point principle for general nonlinear contractions existed unsolved for over 35 years we have solved this problem in this paper

fixed point theorems for multi valued contractions in complete metric spaces abstract in this paper the concept of a contraction for multi valued mappings in a metric space is introduced and the existence theorems for fixed points of such contractions in a complete metric space are proved presented results generalize and improve the recent results of y feng s liu y feng s liu fixed point theorems for multi valued contractive mappings and multi valued caristi type mappings j math anal appl 317 2006 103 112 d klim d wardowski d klim d wardowski fixed point theorems for set valued contractions in complete metric spaces j math anal appl 334 2007 132 139 and several others the method used in the proofs of our results is new and is simpler than methods used in the corresponding papers two examples are given to show that our results are genuine generalization of the results of feng and liu and klim and wardowski

invasion percolation a new form of percolation theory a new kind of percolation problem is described which differs from ordinary percolation theory in that it automatically finds the critical points of the system the model is motivated by the problem of one fluid displacing another from a porous medium under the action of capillary forces but in principle it may be applied to any kind of invasion process which proceeds along a path at least resistance the name invasion percolation is proposed for this new process similarities to and differences from ordinary percolation theory are discussed

fixed point theorems for multi valued contractive mappings and multi valued caristi type mappings abstract in this paper the famous banach contraction principle and caristi s fixed point theorem are generalized to the case of multi valued mappings our results are extensions of the well known nadler s fixed point theorem s b nadler jr multi valued contraction mappings pacific j math 30 1969 475 487 as well as of some caristi type theorems for multi valued operators see n mizoguchi w takahashi fixed point theorems for multivalued mappings on complete metric spaces j math anal appl 141 1989 177 188 j p aubin optima and equilibria an introduction to nonlinear analysis grad texts in math springer verlag berlin 1998 p 17 s s zhang q luo set valued caristi fixed point theorem and ekeland s variational principle appl math mech 10 2 1989 111 113 in chinese english translation appl math mech english ed 10 2 1989 119 121 etc

the contraction principle for set valued mappings on a metric space with a graph let x d be a metric space and f x x be a set valued mapping we obtain sufficient conditions for the existence of a fixed point of the mapping f in the metric space x endowed with a graph g such that the set v g of vertices of g coincides with x and the set of edges of g is e g x y x y xxx

on the relation between the weak palais smale condition and coercivity given by zhong abstract in this paper we discuss zhong s result that the weak palais smale condition implies coercivity under some assumption given in c k zhong a generalization of ekeland s variational principle and application to the study of the relation between the weak p s condition and coercivity nonlinear anal 29 1997 1421 1431 we also give a simple proof of zhong s result further we generalize the result of caklovic li and willem l caklovic s j li m willem a note on palais smale condition and coercivity differential integral equations 3 1990 799 800

some results on set valued contractions in abstract metric spaces abstract in this paper the concept of contractive set valued maps in the frame of abstract metric spaces is studied and the existence of fixed points for such maps is guaranteed under certain conditions consequently several known fixed point results are either generalized or extended including the corresponding recent fixed point results of wardowski d wardowski endpoints and fixed points of set valued contractions in cone metric spaces nonlinear anal 71 2009 512 516 as well as klim and wardowski d klim d wardowski dynamic process and fixed points of set valued nonlinear contractions in cone metric spaces nonlinear anal 71 2009 5170 5175 examples are given to show that our results are distinct from the existing ones

multiple invasion percolation we generalize the standard site invasion percolation model to permit simultaneous invasion of several sites we propose two kinds of generalizations one in which the invasion flux is controlled by the perimeter size and another where the growth process is commanded by the scaling properties the acceptance profile as well as the fractal dimensions df are carefully studied for the model based on scaling relations df can be treated as a mere real parameter in the range 0 in the intervals 0 91 and 2 the system is frustrated for df 2 the model exhibits also an interesting burst phenomenon which is explained in the text in the 91 region 2 the clusters obey exactly and in any scale the relation m rg df between the mass m and the gyration radius rg these stabilized random fractals may be very useful in the study of dilute systems

converses to fixed point theorems of zermelo and caristi let x be an abstract nonempty set and t be a self map of x let per t and fix t denote the sets of all periodic points and all fixed points of t respectively our main theorem says that if pert fixt then there exists a partial ordering such that every chain in x has a supremum and for all x x x tx this result is a converse to zermelo s fixed point theorem we also show that from a purely set theoretical point of view fixed point theorems of zermelo and caristi are equivalent finally we discuss relations between caristi s theorem and its restriction to mappings satisfying caristi s condition with a continuous real function

interpolating sequences for analytic selfmappings of the disc schwarz s lemma leads to a natural interpolation problem for analytic functions from the disc into itself the corresponding interpolating sequences are geometrically described in terms of a certain hyperbolic density

on equivalence of generalized multi valued contractions and nadler s fixed point theorem we consider two generalizations of nadler s theorem one proved by mizoguchi and takahashi in response to the reich conjecture and another theorem proved by kaneko we show that due to the additional conditions of these theorems the given multi valued map reduces to a multi valued contraction map we prove this result by showing that the orbit of the multi valued map is bounded under the contractive conditions of the two generalizations

fixed point theorems for multivalued mappings on complete metric spaces on obtient une version multivaluee du theoreme de point fixe de caristi qui est equivalent au principe e variationnel du a ekeland on utilise ce resultat pour obtenir un theoreme qui deduit le theoreme de nadler et un theoreme de point fixe commun pour une application a 1 valeur et une application multivaluee

fixed point theorems for multi valued contractions with w distance some fixed point theorems for a few nonlinear multi valued contraction mappings in complete metric spaces with w distance are proved the results presented in this paper generalize the recent results due to ciric 2009 3 feng and liu 2006 4 klim and wardowski 2007 8 latif and abdou 2011 12 and liu et al 2010 14 seven examples are given to explain our results

data dependence of the fixed point set of some multivalued weakly picard operators in this paper we study data dependence of the fixed point set for a special class of multivalued weakly picard operators existence and data dependence of the common fixed points for some reich type multivalued operators are also proved finally an application to a fredholm integral inclusion is given

multi valued non self mappings on convex metric spaces abstract in this paper we prove common fixed point theorems for a pair of multi valued non self mappings in metrically convex metric spaces our results generalize and extend both theorems of itoh comment math univ carolin 18 1977 247 and khan pacific j math 95 1981 337 the theorem of assad boll un math ital 4 1973 1 the theorem of rhoades comment math univ carolin 37 1996 401 and the main theorem of assad and kirk pacific j math 43 1972 535

multivalued generalized nonlinear contractive maps and fixed points abstract we introduce some notions of generalized nonlinear contractive maps and prove some fixed point results for such maps consequently several known fixed point results are either improved or generalized including the corresponding recent fixed point results of ciric l b ciric multivalued nonlinear contraction mappings nonlinear anal 71 2009 2716 2723 klim and wardowski d klim d wardowski fixed point theorems for set valued contractions in complete metric spaces j math anal appl 334 2007 132 139 feng and liu y feng s liu fixed point theorems for multivalued contractive mappings and multivalued caristi type mappings j math anal appl 317 2006 103 112 and mizoguchi and takahashi n mizoguchi w takahashi fixed point theorems for multivalued mappings on complete metric spaces j math anal appl 141 1989 177 188

note on a general palais smale condition abstract in this paper we establish a qualitative deformation theorem for a locally lipschitz function satisfying a general palais smale type condition then we show that with some assumptions this compactness condition implies the coercivity of the function

endpoints and fixed points of set valued contractions in cone metric spaces abstract in this paper we introduce the concept of set valued contractions in cone metric spaces and establish new endpoint and fixed point theorems for such contractions the paper includes examples

the strong ekeland variational principle abstract in this paper we consider the strong ekeland variational principle due to georgiev p g georgiev the strong ekeland variational principle the strong drop theorem and applications j math anal appl 131 1988 1 21 we discuss it for functions defined on banach spaces and on compact metric spaces we also prove the distance version of it

the drop theorem the petal theorem and ekeland s variational principle on montre que le principe variationnel d ekeland ou plus precisement une forme legerement modifiee est une consequence d un resultat geometrique connu sous le terme de theoreme de la goutte

fixed point theorems for a broad class of multimaps abstract multimaps from a metric space into the collection of all its nonempty closed subsets are considered and fixed point theorems for such maps have been obtained under new contractive conditions not involving the extended hausdorff metric

non self mappings satisfying non linear contractive condition with applications abstract the concept of non self mappings satisfying a new non linear contractive type condition is introduced and coincidence and common fixed point theorems in metric spaces of hyperbolic type are proved presented theorems generalize and improve recent theorems of imdad and kumar m imdad s kumar rhoades type fixed point theorems for a pair of nonself mappings comput math appl 46 2003 919 927 and several others theorems one example is constructed to show that our theorems are genuine generalizations of the above mentioned results of imdad and kumar and several others

suzuki type fixed point theorems for generalized multi valued mappings on a set endowed with two b metrics abstract in this paper we obtained suzuki type fixed point results for a generalized multi valued mapping on a set equipped with two b metrics as a consequence existence and uniqueness of solution of functional equation arising in dynamical programming is also derived

topology dynamics and finite size effects of a kinetic growth model ramified polymerization is studied through computational simulations on the square lattice of a kinetic growth model generalized to incorporate branching and impurities the polymer configuration is identified with a bond tree in order to examine its topology the fractal dimensions of clusters are obtained at criticality simulations also allow the study of time evolution of clusters as well as the determination of time autocorrelations and dynamical critical exponents in regard to finite size effects a fourth order cumulant technique is employed to estimate the critical branching probability bc and the critical exponents and finally for the case when impurities are not present the surface roughness is described in terms of the hurst exponents

subrahmanyam s fixed point theorem abstract we give a sufficient and necessary condition for the convergence of the sequence of successive approximations to a fixed point which is the conclusion of subrahmanyam s fixed point theorem

remarks on caristi s fixed point theorem abstract in this work we give a characterization of the existence of minimal elements in partially ordered sets in terms of fixed points of multivalued maps this characterization shows that the assumptions in caristi s fixed point theorem can a priori be weakened finally we discuss kirk s problem on an extension of caristi s theorem and prove a new positive result which illustrates the weakening mentioned before