Some Fixed Point Theorems in Metrically Convex Spaces

Abstract

A fixed point theorem is proved in a complete metrically convex metric space. Our result generalizes the theorems of Assad [Tamkang J. Math. 7: 91–94, 1976] and Chatterjea [C.R. Acad., Bulgare Sci. 25: 727–730, 1972].

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.…”

“…By setting S = T = I K in Theorem 3.5, one deduces an extension of a result due to Khan et al [15] to a sequence of multi-valued mappings.…”

“…By setting F n = F (for all n ∈ N) and S = T = I K in Theorem 3.5, one deduces a multi-valued version of a result due to 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].…”

“…Remark 4. Theorem 3.5 of [15], which is a generalization of results of Khan [19] and Khan et al [20], follows from Example 1 and Theorem 2.…”