Common Fixed Points in Modular Spaces

Abstract

In this paper,there are new considerations about the dual of a modular spaces and weak convergence. Two common fixed point theorems for a -non-expansive mapping defined on a star-shaped weakly compact subset are proved, Here the conditions of affineness, demi-closedness and Opial's property play an active role in the proving our results.

Multi-Step Iteration Algorithm of Total Asymptotically Quasi-Nonexpansive Maps

“…One can study convergence theorems in (1) and in [17, theorem (11)] for families of general asymptotic set-valued maps. As well as possible to demonstrate new results in the case of other spaces as a modular space [18].…”

Approximating fixed points in modular spaces

“…Suppose that {u n } as in (5) converges to point p, where a n þ b n ¼ 1; cnand lim n/∞ infa n > 0 {x n },{m n } satisfying (13). If for all n sufficiently large, S and T satisfy (14), (15) and (16). Then p is a common fixed point for S and T Proof: Use condition (5) u nþ1 ¼ ð1À a n Þu n þ a n m n ; m n 2Sv n .…”

“…(g) The distance between v 2 M g and B3M g is gðvÀ BÞ ¼ inffgðvÀ uÞ; u 2 Bg. Definition 1.5 [14] Let m g be a modular space, and A; B are two non e empty subsets of m g . Let H g ðA; BÞ denotes the Hausdorff distance of A and B that is defined as the following:…”

Integral Transforms of New Subclass of Meromorphic Univalent Functions Defined by Linear Operator I

“…Several properties are resulted such as, coefficient estimates, convex set, extreme point and obtain some interested results. See also References [5][6][7][8][9].…”