A Unique Common Triple Fixed Point Theorem for Hybrid Pair of Maps

Abstract

We obtain a unique common triple fixed point theorem for hybrid pair of mappings in metric spaces. Our result extends the recent results of B. Samet and C. Vetro (2011). We also introduced a suitable example supporting our result.

n-tuplet fixed points of multivalued mappings via measure of noncompactness

“…If we take as special cases n = 2 and n = 3 in Definition 3.1, respectively, we get coupled fixed points [17] and tripled fixed points [18]. Theorem 3.3.…”

“…The concept of coupled fixed points for multivalued mappings was introduced by Samet and Vetro [17] and they obtained coupled fixed point theorems for multivalued nonlinear contraction mappings in a partially ordered metric space. Rao, Kishore and Kenan [18] obtained a tripled coincidence fixed point theorem for multivalued mappings in a partially ordered metric space.…”

On n-tuplet fixed points for noncompact multivalued mappings via measure of noncompactness

“…Remark 1. If we take as special cases n = 2 and n = 3 in the Definition 5, respectively, we get coupled fixed point (see; [28]) and tripled fixed point (see; [29]).…”

“…The concept of coupled fixed point for multivalued mappings was introduced by Samet and Vetro [28] and they presented coupled fixed point theorem for multivalued nonlinear contraction mappings in partially ordered metric space. Rao et al [29] obtained a tripled coincidence fixed point theorems for multivalued mappings in partially ordered metric space.…”

Multi-valued tripled fixed point results via CLR property in metric spaces with application

“…Rao et al [15] obtained a unique common triple fixed point theorem for hybrid pair of mappings in metric spaces. Aydi and Abbas [4] introduced the concept of w-compatiblity for single-valued tripled hybrid mappings.…”