*Correspondence: [email protected] School of Science, Sichuan University of Science and Engineering, Zigong, Sichuan 643000, China Abstract We prove quadruple fixed point theorems in partially ordered metric spaces with mixed g-monotone property. Also, we state some examples to show that our results are real generalization of known ones in quadruple fixed point theory. MSC: 46T99; 54H25; 47H10;...

The Schauder conjecture that every continuous single-valued map from a compact convex subset of a topological vector space into itself has a fixed point was stated in [12, Problem 54]. In a recent year, Cauty [2] gave a positive answer to this question by a very complicated approximation factorization. Very recently, Dobrowolski [3] established Cauty’s proof in a more accessible form by using t...

The purpose of this paper is to establish some coupled coincidence point theorems for a pair of mappings having a mixed g-monotone property satisfying a contractive condition of rational type in the framework of partially ordered metric spaces. Also, we present a result on the existence and uniqueness of coupled common fixed points. The results presented in the paper generalize and extend sever...

In this paper, coupled xed point results of Bhaskar-Lakshmikantham type [T. Gnana Bhaskar, V.Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, NonlinearAnalysis 65 (2006) 1379-1393] are extend, generalized, unify and improved by using monotonemappings instead mappings with mixed monotone property. Also, an example is given to supportthese improvements.

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In this paper, we introduce a new geometric property (UÃ2) and we show that if a separable Banach space has this property, then both X and its dual X∗ have the weak fixed point property. We also prove that a uniformly Gateaux differentiable Banach space has property (UÃ2) and that if X∗ has property (UÃ2), then X has the (UKK)-property. Criteria for Orlicz spaces to have the properties (UA2), (...

We show the existence of an infinite monothetic Polish topological group G with the fixed point on compacta property. Such a group provides a positive answer to a question of Mitchell who asked whether such groups exist, and a negative answer to a problem of R. Ellis on the isomorphism of L(G), the universal point transitive G-system (for discrete G this is the same as PG the Stonetech compacti...

Suppose K is a closed convex subset of a real reflexive Banach space E which has a uniformly Gâteaux differentiable norm and every nonempty closed convex bounded subset of E has the fixed point property for nonexpansive mappings. We prove a strong convergence theorem for an m−accretive mapping from K to E. The results in this paper are different from the corresponding results in [8] and they im...