comparison theorems for linear dynamic equations on time scales we obtain several comparison theorems for second order linear dynamic equations on a time scale these results extend comparison theorems for the continuous case and provide some new results in the discrete case as well as other more general situations

on quadratic integral equation of fractional orders abstract we present an existence theorem for a nonlinear quadratic integral equations of fractional orders arising in the queuing theory and biology in the banach space of real functions defined and continuous on a bounded and closed interval the concept of measure of noncompactness and a fixed point theorem due to darbo are the main tool in carrying out our proof

a geometric property of banach spaces related to the fixed point property abstract in this note we give a sufficient condition for the fixed point property for nonexpansive mappings in banach spaces which we call the amcp this property is more general than normal structure and the space c 0 james space as well as every banach space endowed with a suitable schauder basis also have the amcp on the other hand a renorming of the tsirelson space and also 1 lack the amcp

a universal infinite dimensional modulus for normed spaces and applications abstract we define an infinite dimensional modulus which can be simultaneously considered as a measure of nearly uniform convexity and nearly uniform smoothness we compute this modulus in some classical banach spaces and we show some basic properties of this modulus and some applications to prove that a banach space satisfies the w fixed point property for non expansive mappings

fixed point property of direct sums abstract for a uniformly convex space z we show that z direct sums x 1 x n z of banach spaces x 1 x n with r a x i 1 a for some a 0 1 have the fixed point property for nonexpansive mappings as a direct consequence the result holds for all direct sums with being strictly convex the same result is extended to all direct sums x y of spaces x and y with property m whenever 1 the permanence of properties that are sufficient for the fixed point property are obtained for z direct sums and then for direct sums such properties include the properties r x 2 wnus c nj a x 2 ukk and nuc

transmutation method for solving erdelyi kober fractional differintegral equations abstract by means of fractional calculus techniques we find explicit solutions of volterra integral equations of the second kind and fractional differential and differintegral equations involving erdelyi kober fractional integrals and derivatives also some hypergeometric integral equations have been considered and solved as double erdelyi kober equations of the second kind we use the transmutation method to reduce the solutions of all these equations to known solutions of simpler riemann liouville equations of the same type some examples are given

fixed point property for banach algebras associated to locally compact groups abstract in this paper we investigate when various banach algebras associated to a locally compact group g have the weak or weak fixed point property for left reversible semigroups we proved for example that if g is a separable locally compact group with a compact neighborhood of the identity invariant under inner automorphisms then the fourier stieltjes algebra of g has the weak fixed point property for left reversible semigroups if and only if g is compact this generalizes a classical result of t c lim for the case when g is the circle group t

oscillation for nonlinear second order dynamic equations on a time scale abstract we obtain some oscillation criteria for solutions to the nonlinear dynamic equation x q t x p t f x 0 on time scales in particular no explicit sign assumptions are made with respect to the coefficients p t q t we illustrate the results by several examples including a superlinear emden fowler dynamic equation

weak fixed point property of reduced fourier stieltjes algebra and generalization of baggett s theorem abstract in this paper we show that if the reduced fourier stieltjes algebra b g of a second countable locally compact group g has either weak fixed point property or asymptotic center property then g is compact as a result we give affirmative answers to open problems raised by fendler and et al in 2013 we then conclude that a second countable group with a discrete reduced dual must be compact this generalizes a theorem of baggett we also construct a compact scattered hausdorff space for which the dual of the scattered c algebra c lacks weak fixed point property the c algebra c provides a negative answer to a question of randrianantoanina in 2010 in addition we prove a variant of bruck s generalized fixed point theorem for the preduals of von neumann algebras furthermore we give some examples emphasizing that the conditions in bruck s generalized conjecture bgc can not be weakened any more

nondecreasing solutions of a quadratic abel equation with supremum in the kernel we prove an existence theorem for a quadratic abel integral equation of the second kind with supremum in the kernel the quadratic integral equation studied below contains as a special case numerous integral equations encountered in the theory of radiative transfer and in the kinetic theory of gases we show that the singular quadratic integral equations with supremum has a monotonic solution in c 0 1 the concept of measure of noncompactness and a fixed point theorem due to darbo are the main tools in carrying out our proof

on erdelyi kober type quadratic integral equation with linear modification of the argument abstract in this paper we study the existence of solutions for a nonlinear erdelyi kober fractional quadratic integral equations with linear modification of the argument the main tool used in our considerations is the technique associated to measures of noncompactness we compare our results with the ones obtained in recent papers finally we present some examples illustrating our results

asymptotic behavior of solutions of a third order nonlinear dynamic equation on time scales in this paper we will establish some sufficient conditions which guarantee that every solution of the third order nonlinear dynamic equation c t a t x t q t f x t 0 t t0 oscillates or converges to zero

calculus of variations on time scales weak local piecewise crd1 solutions with variable endpoints abstract a nonlinear calculus of variations problem on time scales with variable endpoints is considered the space of functions employed is that of piecewise rd continuously differentiable functions c1prd for this problem the euler lagrange equation the transversality condition and the accessory problem are derived as necessary conditions for weak local optimality assuming the coercivity of the second variation a corresponding second order sufficiency criterion is established

new kamenev type oscillation criteria for second order differential equations on a measure chain we establish new kamenev type criteria for oscillation of the second order linear differential equation p t x d t d q t x s t 0 on a measure chain our results are extensions of those for differential equations and provide new oscillation criteria for difference equations several examples are given to show the significance of the results

some estimates for the weakly convergent sequence coefficient in banach spaces we present relations between the weakly convergent sequence coefficient of a banach space and other coefficients some estimates are sharp

on erdelyi kober fractional urysohn volterra quadratic integral equations a very general nonlinear singular integral equation is introduced namely u f 1 u f 2 u 0 s 1 k s a u s s 1 d s 0 1 0 and 0 1 the above equation is called erdelyi kober fractional urysohn volterra quadratic integral equation the main goal is to show that the above equation has solutions in c0 1 and these solutions are nonnegative and nondecreasing on 0 1 by means of a measure of noncompactness and darbo fixed point theorem we prove our main results in the end of the paper we give an example to show that our assumptions of our abstract results are rather easy to verify

on james and von neumann jordan constants and sufficient conditions for the fixed point property abstract in this paper we prove that a banach space x and its dual space x have uniform normal structure if c nj x 1 3 2 the garcia falset coefficient r x is estimated by the c nj x constant and the weak orthogonality coefficient introduced by b sims finally we present an affirmative answer to a conjecture by l maligranda concerning the relation between the james and c nj x constants for a banach space

on a quadratic fractional hammerstein volterra integral equation with linear modification of the argument abstract we study the existence of monotonic solutions of a quadratic fractional hammerstein volterra integral equation with linear modification of the argument the quadratic integral equation studied below contains as a special case numerous integral equations encountered in the theory of radiative transfer and in the kinetic theory of gases we show that the quadratic fractional hammerstein volterra integral equation with linear modification of the argument has a monotonic solution in the banach space of all real functions defined and continuous on a bounded and closed interval the concept of measure of noncompactness and a fixed point theorem due to darbo are the main tools in carrying out our proof

the fixed point property in banach spaces with the nus property abstract in this paper we show that the weak nearly uniform smooth banach spaces have the fixed point property for nonexpansive mappings

an equation of hammerstein type arising in particle transport theory an equation of hammerstein type arising in particle transport theory is derived a sufficient condition for the existence of a solution to it is obtained via a simple application of the contracting mapping principle

oscillation and nonoscillation of solutions of second order linear dynamic equations with integrable coefficients on time scales we obtain willett wong type oscillation and nonoscillation theorems for second order linear dynamic equations with integrable coefficients on a time scale the results obtained extend and are motivated by oscillation and nonoscillation results due to willett 20 and wong 21 for the second order linear differential equation as applications of the new results obtained we give the complete classification of oscillation and nonoscillation for the difference email protected 2x n b 1 nt cx n 1 0 email protected 2x n at c 1 b 1 nt cx n 1 0for email protected n a b email protected r we also improve a nonoscillation result of mingarelli 17 and extend an oscillation result of del medico and kong 7

relationships between properties that imply the weak fixed point property a number of banach space properties have previously been shown to imply the weak fixed point property we investigate various connections between these properties

on the euler sequence spaces which include the spaces l p and l i in the present paper we introduce the euler sequence space e p r consisting of all sequences whose euler transforms of order r are in the space p of non absolute type which is the bk space including the space p and prove that the spaces e p r and p are linearly isomorphic for 1

oscillation of second order half linear delay dynamic equations with damping on time scales by using the generalized riccati transformation and the inequality technique we establish a few new oscillation criterions for certain second order half linear delay dynamic equations with damping on a time scale our results extend and improve some known results but also unify the oscillation of the second order half linear delay differential equation with damping and the second order half linear delay difference equation with damping

uniformly nonsquare banach spaces have the fixed point property for nonexpansive mappings abstract it is shown that if the modulus x of nearly uniform smoothness of a reflexive banach space satisfies x 0 1 then every bounded closed convex subset of x has the fixed point property for nonexpansive mappings in particular uniformly nonsquare banach spaces have this property since they are properly included in this class of spaces this answers a long standing question in the theory

properties ua 2 and wa 2 in orlicz spaces and some of their consequences abstract we introduce a new geometric property a 2 and we show that it is equivalent to its uniform version u a 2 next we introduce a new property u a 2 and we show that if a separable banach space x has this property then both x and x have the weak fixed point property we also prove that a uniformly gateaux differentiable banach space has property u a 2 and that if x has property u a 2 then x has the ukk property criteria in order that orlicz spaces have the properties u a 2 u a 2 and nus are given

oscillation theorems for second order half linear delay dynamic equations with damping on time scales by using the generalized riccati transformation and the inequality technique we establish a few new oscillation criteria for certain second order half linear delay dynamic equations with damping on a time scale our results extend and improve some known results but also unify the oscillation of the second order half linear delay differential equation with damping and the second order half linear delay difference equation with damping

oscillatory behavior of third order nonlinear delay dynamic equations on time scales in this paper a class of third order nonlinear delay dynamic equations on time scales is studied by using the generalized riccati transformation and the integral averaging technique three new sufficient conditions which ensure that every solution is oscillatory or converges to zero are established the results obtained essentially generalize and improve earlier ones

kamenev type and interval oscillation criteria for second order linear differential equations on a measure chain abstract we establish kamenev type criteria and interval criteria for oscillation of the second order scalar differential equation p t x t q t x t 0 on a measure chain our results cover those for differential equations and provide new oscillation criteria for difference equations several examples are given to show the significance of the results

wong s comparison theorem for second order linear dynamic equations on time scales we obtain wong type comparison theorems for second order linear dynamic equations on a time scale the results obtained extend and are motivated by wong s comparison theorems as a particular application of our results we show that the difference equation

nearly uniformly noncreasy banach spaces we introduce and study the class of nearly uniformly noncreasy banach spaces it is proved that they have the weak fixed point property a stability result for this property is obtained

absolute continuity and existence of solutions to dynamic inclusions in time scales we provide some properties for absolutely continuous functions in time scales then we consider a class of dynamical inclusions in time scales and extend to this class a convergence result of a sequence of almost inclusion trajectories to a limit which is actually a trajectory of the inclusion in question we also introduce the so called euler solution to dynamical systems in time scales and prove its existence a combination of the existence of euler solutions with the compactness type result described above ensures the existence of an actual trajectory for the dynamical inclusion when the setvalued vector field is nonempty compact convex and has closed graph

oscillation of second order nonlinear delay dynamic equations on time scales by using the generalized riccati transformation and the inequality technique we establish one new oscillation criterion for the second order nonlinear delay dynamic equations on time scales our results not only extend and improve some known theorems but also unify the oscillation of the second order nonlinear delay differential equation and the second order nonlinear delay difference equation on time scales

neocompact sets and the fixed point property abstract we use a newly introduced concept of neocompactness to study problems from metric fixed point theory in particular we give a sufficient condition for a superreflexive banach space x to have the fixed point property and obtain shorter proofs of some well known results in that theory