We establish a Julia–Carathéodory theorem and a boundary Schwarz– Wolff lemma for hyperbolically monotone mappings in the open unit ball of a complex Hilbert space. Let B be the open unit ball of a complex Hilbert space H with inner product 〈·, ·〉 and norm ‖ · ‖, and let ρ : B ×B 7→ R be the hyperbolic metric on B ([8], p. 98), i.e., ρ(x, y) = tanh √ 1− σ(x, y), (1) where σ(x, y) = (1 − ‖x‖)(1 ...

The common fixed point results for Banach operator pair with generalized nonexpansive mappings in q-normed space have been obtained in the present work. As application, some more general best approximation results have also been determined without the assumption of linearity or affinity of mappings. These results unify and generalize various existing known results with the aid of more general c...

Keywords: Implicit iterative algorithm Asymptotically quasi-nonexpansive mappings Common fixed point Convex metric space a b s t r a c t In this paper, we consider an implicit iteration process to approximate the common fixed points of two finite families of asymptotically quasi-nonexpansive mappings in convex metric spaces. As a consequence of our result, we obtain some related convergence the...

In this paper, we introduce a new iterative scheme to approximate a common fixed point for a finite family of nonexpansive non-self mappings. Strong convergence theorems of the proposed iteration in Banach spaces.

Nonexpansive mappings have been studied extensively in recent years by many authors.The first fixed point theorem of a general nature for nonlinear nonexpansive mappings in noncompact setting were proved independently by Browder [8] and Gohde [12]. Later on, Kirk [17] proved the same results under slightly weaker assumptions. A fundamental problem in fixed point theory of nonexpansive mappings ...

The study of fixed points for multivalued contractions and nonexpansive maps using the Hausdorff metric was initiated by Markin [17]. Later, an interesting and rich fixed point theory for such maps has been developed. The theory of multivalued maps has applications in control theory, convex optimization, differential inclusions, and economics (see, e.g., [3, 8, 16, 22]). The theory of multivalu...

In this paper, we introduce the iterative method for finding a common element of the set of solutions of a generalized equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space and then obtain the sequence converges strongly to a common element of two sets. The results extended and improved the corresponding results of Plubtieng and Punpaeng [S. Plubtieng, R. ...

In this paper, we prove a convergence theorem for Passty type asymptotically nonexpansive mappings in a uniformly convex Banach space with Fréchet-differentiable norm.

A one-step iteration with errors is considered for a family of asymptotically nonexpansive nonself mappings. Weak convergence of the purposed iteration is obtained in a Banach space.

In this paper, we introduce new classes of proximal multi-valued contractions in a metric space and nonexpansive mappings Banach show the existence best proximity points for both classes. Further, mappings, prove point theorem on starshape sets. As consequence, also obtain some fixed theorems. Finally, give examples to illustrate our main results.