Fixed point theorems for a family of hybrid pairs of mappings in metrically convex spaces

Abstract

The present paper establishes some coincidence and common fixed point theorems for a sequence of hybrid-type nonself-mappings defined on a closed subset of a metrically convex metric space. Our results generalize some earlier results due to Khan et al. (2000), Itoh (1977), Khan (1981), Ahmad and Imdad (1992 and 1998), and several others. Some related results are also discussed

Some Fixed Point Theorems for Multivalued Maps Satisfying an Implicit Relation on Metrically Convex Spaces

“…The purpose of this paper is to prove some coincidence and common fixed point theorems for multivalued mappings satisfying an implicit relation on metrically convex spaces. Our results either partially or completely generalize earlier results due to Ahmad and Imdad [1], [2], Ahmad and Khan [3],Ćirić [7], Imdad and Khan [15], Itoh [17], Khan [19], Khan et al [20], Rhoades [26] and several others. See also the related Theorem 3.1 of [14].…”

“…Remark 5. Corollary 3.6 of [15], which is a generalization of results of [8], follows from Example 1 and Theorem 3.…”

“…Remark 2. Theorem 3.1 of [15], which is a generalization of results of [1], [2], follows from Example 1 and Theorem 1. Moreover, (F i , T ) has a common fixed point if T is quasi-coincidentally commuting and coincidentally idempotent w.r.t.…”

Weak condition for generalized multi-valued (f,α,β)-weak contraction mappings

“…Nadler's fixed point theorem [2] and Theorem 2.1 in [21] are particular cases of Theorem 1.3. Later many authors studied and proved some coincidence and common fixed point theorems; for example, see, [22][23][24]7,25,8,4,26,2,[27][28][29] and the references therein. In 2006, Beg and Abbas [30] proved the existence of a coincidence point and a common fixed point for mappings satisfying generalized weak contractive condition.…”