Let X be a uniformly convex Banach space and S {T s : 0 ≤ s < ∞} be a nonexpansive semigroup such that F S ⋂s>0 F T s / ∅. Consider the iterative method that generates the sequence {xn} by the algorithm xn 1 αnf xn βnxn 1 − αn − βn 1/sn ∫sn 0 T s xnds, n ≥ 0, where {αn}, {βn}, and {sn} are three sequences satisfying certain conditions, f : C → C is a contraction mapping. Strong convergence of t...

We present some fixed point results for a single mapping and a pair of compatible mappings via auxiliary functions which satisfy a generalized weakly contractive condition in partially ordered complete $G$-metric spaces. Some examples are furnished to illustrate the useability of our main results. At the end, an application is presented to the study of exi...

Cantor's naive set theory is characterized by the unrestricted comprehension principle, saying that for every formula A(x), there exists a set {x|A(x)} such that A(t) ↔ t ∈ {x|A(x)} for any term t. The theory is intuitive, elegant, powerful, but unfortunately inconsistent (as witnessed by Russell's paradox). While it is common to somehow restrict the comprehension scheme (as in ZFC), there is a...

in this paper, we establish and prove the existence of best proximity points for multivalued cyclic $f$- contraction mappings in complete metric spaces. our results improve and extend various results in literature.

recently, choudhury and metiya [fixed points of weak contractions in cone metric spaces, nonlinear analysis 72 (2010) 1589-1593] proved some fixed point theorems for weak contractions in cone metric spaces. weak contractions are generalizations of the banach's contraction mapping, which have been studied by several authors. in this paper, we introduce the notion of $f$-weak contractions and als...

Some fixed and coincidence point theorems for R-weakly commuting mappings are obtained. Our results generalize some recent results of Daffer and Kaneko [2] and many of the others. AMS Mathematics Subject Classification (2000): 54H25

a) X is strongly paracompact; b) X is paracompact; c) X is metacompact; d) X is weakly θ-refinable; e) Every open cover of X has a point-countable open refinement; f) X is subparacompact; g) If C is a closed subspace of X, then there are discrete closed sets S and T which are, respectively, well-ordered and reverse-well-ordered by the given ordering of X, have S ∪ T ⊂ C, and have the property t...

*Correspondence: [email protected] Department of Mathematics, Hashemite University, Zarqa, Jordan Abstract In this paper, we prove some quadruple coincidence and quadruple common fixed point theorems for F : X4 → X and g : X → X satisfying (φ –ψ ) contractions in partially ordered G-metric spaces. We illustrate our results based on an example of the main theorems. Also, we deduce quadruple coi...