In this paper, we establish coupled best proximity point theorems for multivalued mappings. Our results extend some recent results by Ali et al. (Abstr. Appl. Anal. 2014:181598, 2014 as well as other results in the literature. We also give examples to support our main results. MSC: 47H09; 47H10

S-metric space is considered to be a generalization of a G-metric space and a D *-metric space and it proved to be a rich source for fixed point theory; however, the best proximity point problem remains open in such spaces. The aim of this paper is to establish the best proximity point results for a class of proximal contractive mappings in S-metric spaces. We provide examples to analize and support our results.

In this paper, we use the concept of C-class functions to establish the best proximity point results for a certain class of proximal contractive mappings in S-metric spaces. Our results extend and improve some known results in the literature. We give examples to analyze and support our main results.MSC: Primary 47H10; secondary 54H25

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In this manuscript, we investigate and approximate common fixed points of two asymptotically quasi-nonexpansive mappings in CAT0 spaces. Suppose X is a CAT0 space and C is a nonempty closed convex subset of X. Let T1,T2:C→C be two asymptotically quasi-nonexpansive mappings, and F=FT1∩FT2≔x∈C:T1x=T2x=x≠∅. Let αn,βn be sequences in 01. If the sequence {xn} is generated iteratively by xn+1=1−αnxn⊕αnT1nyn,yn=1−βnxn⊕βnT2nxn,n≥1 and x1∈C is the initial element of the sequence (A). We prove that {xn} converges strongly to a common fixed point of T1 and T2 if and only if limn→∞dxnF=0. (B). Suppose αn and βn are sequences in ε1−ε forsome ε∈01. If X is uniformly convex and if either T2 or T1 is compact, then {xn} converges strongly to some common fixed point of T1 and T2. Our results extend and improve the related results in the literature. We also give an example in support of our main results.

In this paper, we study multi-step iterative algorithm with errors for p+1 asymptotically nonexpansive mappings in uniformly convex Banach spaces. Also we have proved weak and strong convergence theorems for the mentioned algorithm. The results presented in this paper improve and extend the corresponding results of Khan and Fukhar-ud-din [6], Keywords: Asymptotically nonexpansive mappings; Common fixed points; Opial's condition; Multi-step iterative algorithm with errors; Uniformly convex Banach space Case 1. Suppose that x and y ∈ [0, 1]. It follows that |x − T 1 y| = |x + sin y| = |Rx − T 1 y|; Case 2. Suppose that x and y ∈ [−1, 0). It follows that |x − T 1 y| = |x − sin y| ≤ | − x − sin y| = |Rx − T 1 y|; Case 3. Suppose that x ∈ [−1, 0) and y ∈ [0, 1]. It follows that |x − T 1 y| = |x + sin y| ≤ | − x + sin y| = |Rx − T 1 y|; Case 4. Suppose that x ∈ [0, 1] and y ∈ [−1, 0). It follows that |x − T 1 y| = |x − sin y| = |Rx − T 1 y|;Hence (13) is satisfied. Thus Theorems 3.1 and 13 implies that the {x n } defined by (8) converges both strongly and weakly to 0, respectively. ACKNOWLEDGEMENTS. The authors would like to thank LampangRajabhat University and Rajabhat Maha Sarakham University for financial supports during the preparation of this paper. Moreover, the authors would like to thank the referees for their useful comments for the improvement of this paper.

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In this manuscript, we investigate and approximate common fixed points of two nonself asymptotically nonexpansive mappings in the setting of CAT(0) spaces. We provide three examples and conduct numerical experiments to show the implementation of the approximation schemes. Our results extend and improve the related results in the literature.