In this paper, we introduce some concepts in partial b-metric spaces. We establish fixed point theorems for some new generalized α − ψ type contractive mappings in the setting of partial b-metric spaces. Some examples are presented to illustrate our obtained results. Finally, we show that the results generalize some recent results. c ©2016 All rights reserved.

The fixed point alternative methods are implemented to give generalized Hyers-Ulam-Rassias stability for the Pexiderized quadratic functional equation in the fuzzy version. This method introduces a metrical context and shows that the stability is related to some fixed point of a suitable operator.

Abstract. This paper deals with fixed point theory and fixed point property in minimal spaces. We will prove that under some conditions f : (X,M) → (X,M) has a fixed point if and only if for each m-open cover {Bα} for X there is at least one x ∈ X such that both x and f(x) belong to a common Bα. Further, it is shown that if (X,M) has the fixed point property, then its minimal retract subset enj...

Recall that a vector norm on R is a mapping ‖·‖ : R → R satisfying the following conditions: • ‖x‖ > 0 for x 6= 0. • ‖λx‖ = |λ|‖x‖ for x ∈ R and λ ∈ R. • ‖x+ y‖ ≤ ‖x‖+ ‖y‖ for all x, y ∈ R. Since the space Rn×n of all matrices is also a vector space, it is also possible to consider norms there. In contrast to usual vectors, it is, however, also possible to multiply matrices (that is, the matric...

This algorithm supports line clipping against a rectangular window with edges parallel to the screen. The algorithm combines different partial solutions given in the bibliography such as implicit area codes, decision trees, line ends comparison, symmetry or avoiding redundant calculations, mixing them with fixed-point arithmetic, explicit calculation reusing and dynamic monitoring. It may work ...

We consider the problem of estimating numerical accuracy programs with operations in fixed-point arithmetic and variables arbitrary, mixed precision, possibly non-deterministic value. By applying a set parameterised rewrite rules, we transform relevant fragments program under consideration into sequences integer over vectors bits, thereby reducing as to whether error enclosures initial can ever...