Some Common Fixed Point Theorems for Non-self Hybrid Contractions

Abstract

Some results on the common fixed point for a pair of multivalued and single valued non-self mappings in metrically convex metric spaces are obtained. Our work extends some of the known results due to Assad and Kirk, Hadzic and Gajic, Itoh, Khan, and many others.ᮊ 1997 Academic Press

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

“…The purpose of this paper is to prove some coincidence and common fixed point theorems for a sequence of hybrid type nonself mappings satisfying certain contraction type condition which is essentially patterned after Khan et al [15]. Our results either partially or completely generalize earlier results due to Khan et al [15], Itoh [12], Khan [14], Ahmad and Imdad [1,2], Ahmad and Khan [3] and several others.…”

“…Most recently, Huang and Cho [9] and Dhage et al [6] proved some fixed point theorems for a sequence of set-valued mappings which generalize several results due to Itoh [12], Khan [14], Ahmad and Khan [3] and others. The purpose of this paper is to prove some coincidence and common fixed point theorems for a sequence of hybrid type nonself mappings satisfying certain contraction type condition which is essentially patterned after Khan et al [15].…”

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].…”

“…In the current years the work due to Assad and Kirk [6] has inspired extensive activities which includes Ahmad and Imdad [1], [2], Imdad et al [13], Imdad and Ali [14], Itoh [17], Khan [19] and some others. Most recently, Dhage et al [9] and Huang and Cho [12] proved some fixed point theorems for a sequence of set-valued mappings which generalize several results due to Ahmad and Khan [3], Itoh [17], Khan [19] and others. 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.…”

On two pairs of non-self hybrid mappings

“…In the last four decades several authors have proved some fixed point or common fixed point theorems for self-mappings (see, for example, [5], [12,13], [15][16][17], [20]), or for non-self mappings (see, for example, [1][2][3][4]9], [6][7][8]10,11], [14], [18,19], [21].) Some applications of non-self mappings are given by Assad and Kirk [4] and by Tsachev and Angelov [21].…”