## 1 Introduction
For this purpose, different iteration processes, i.e.,those of [PERSON] [17], [PERSON] [18], [PERSON] [19], [PERSON] [20], [PERSON] [21], [PERSON] [22], CR [23], Normal-\(S\)[24], Thakur New [25] and M-iteration [26], etc., have been introduced. The approximating of a fixed point using an effective iterative technique is an important field of research. For instance, [PERSON] and [PERSON] [27] studied [PERSON] iterative scheme for G-nonexpansive operators while [PERSON] [28] proved strong convergence of a certain scheme for variational inequalities problems. Moreover, different authors made claims about the convergence speed of their iteration processes: according to the authors in [19], the [PERSON] iteration converges faster than [PERSON]'s and has the same convergence speed as the [PERSON] iteration. In [21], the author proved that the iteration process of [PERSON] converges faster than [PERSON]'s. Similarly, according to [PERSON] and [PERSON] [29], the Picard-S iterative process is converge than the [PERSON], Ishikawa, Noor, SP, CR, Normal-S iteration processes. The author proved in [25] that the Thauker-New iterative process is fast in terms of convergence when compared to [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], and [PERSON] iteration processes for [PERSON] generalized nonexpansive mappings. In 2018, [PERSON] and [PERSON] [26] proved that, compared to all the above mentioned iteration processes, newly introduced M-iteration processes have high speeds of convergence for Suzuki generalized nonexpansive mappings. For multi-valued nonexpansive mappings, initially, [PERSON] and [PERSON] [30] worked on the convergence of [PERSON] and [PERSON] iterative processes in Hilbert spaces. [PERSON] and [PERSON] [31] (cf. also [PERSON] and [PERSON] [32] and others) introduced \(P_{\mathbb{J}}(a^{\prime})=\{b^{\prime}\in\mathbb{J}(a^{\prime}):d(a^{\prime}, \mathbb{J}a^{\prime})=||a^{\prime}-b^{\prime}||\}\) for multi-valued mappings \(\mathbb{J}:B\to P(B)\) and also proved convergence of Ishikawa iteration process in a UCBS. Consider a multi-valued mapping \(\mathbb{J}:B\to P(B)\). Choose \(\alpha_{n},\beta_{n},\gamma_{n}\in(0,1)\). We list here multi-valued versions of [PERSON] [22], [PERSON] [33], [PERSON] [21], and [PERSON] [29], respectively, as follows:  
\[\left\{ \begin{array}{l}k_{1}\in B,\\ k_{n+1}=(1-\alpha_{n})k_{n}+\alpha_{n}v_{n},\\ l_{n}=(1-\beta_{n})k_{n}+\beta_{n}w_{n},\\ m_{n}=(1-\gamma_{n})k_{n}+\gamma_{n}h_{n},\end{array} \right. \tag{1}\]where \(u_{n}\in P_{\mathbb{J}}(k_{n})\), \(w_{n}\in P_{\mathbb{J}}(m_{n})\) and \(v_{n}\in P_{\mathbb{J}}(l_{n})\). \[\left\{ \begin{array}{l}k_{1}\in B,\\ k_{n+1}=v_{n},\\ l_{n}=(1-\alpha_{n})k_{n}+\alpha_{n}u_{n},\end{array} \right. \tag{2}\]  
where \(u_{n}\in P_{\mathbb{J}}(k_{n})\) and \(v_{n}\in P_{\mathbb{J}}(l_{n})\). \[\left\{ \begin{array}{l}k_{1}\in B,\\ k_{n+1}=(1-\alpha_{n})v_{n}+\alpha_{n}w_{n},\\ l_{n}=(1-\beta_{n})u_{n}+\beta_{n}w_{n},\\ m_{n}=(1-\gamma_{n})k_{n}+\gamma_{n}u_{n},\end{array} \right. \tag{3}\]  
where \(u_{n}\in P_{\mathbb{J}}(k_{n})\), \(w_{n}\in P_{\mathbb{J}}(m_{n})\) and \(v_{n}\in P_{\mathbb{J}}(l_{n})\). The multi-valued version of the \(M\)-iterative process reads as follows:  
\[\left\{ \begin{array}{l}k_{1}\in B,\\ k_{n+1}=v_{n},\\ l_{n}=w_{n},\\ m_{n}=(1-\alpha_{n})k_{n}+\alpha_{n}u_{n},\end{array} \right. \tag{4}\]  
where \(u_{n}\in P_{\mathbb{J}}(k_{n})\), \(w_{n}\in P_{\mathbb{J}}(m_{n})\) and \(v_{n}\in P_{\mathbb{J}}(l_{n})\). [PERSON] et al. [34] used this scheme for finding fixed points of multi-valued \(\alpha\)-nonexpansive maps. Here, using (4), we will provide weak and strong convergence results for the class of multi-valued generalized \((\alpha,\beta)\)-nonexpansive mappings. The results will be supported by examples. **2. Preliminaries**  
Let \(B\) be a subset of a Banach space and \(\mathbb{J}:B\to S(B)\).