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In this paper we prove the existence and uniqueness of coincident (fixed) points for nonlinear mappings of any number of arguments under a (ψ, θ, φ)-weak contraction condition without O-compatibility. The obtained results extend, improve and generalize some well-known results in the literature to be discussed below. Moreover, we present an example to show the efficiency of our results.

Altun, Ishak/0000-0002-7967-0554; WOS: 000408468300010 In this paper, taking into account the recent contractive technique, which was introduced by Wardowski [18], we present a fixed point theorem for F-contractive type fuzzy mappings over a complete metric space. Kirikkale University, Turkey [2016/117] This research was supported by Kirikkale University project number 2016/117, Turkey. The authors are thankful to the referees for making valuable suggestions leading to the better presentations of the paper.

In this work, we introduce the new concepts of fuzzy (h, β)-contractive mapping via triangular (h, β)-admissible mappings. Later, we prove some fixed point results for some mappings that provide fuzzy (h, β)-contractibility and triangular (h, β)-admissibility in complete non-Archimedean fuzzy metric spaces. Some examples are supplied in order to support the applicability of our results. Our main results substantially generalize and extend some known results in the existing literature.

The main objective of this work is to develop fixed point results for (alpha, phi)-Meir-Keeler contractive mappings in generalized rectangular b-metric spaces and to investigate the uniqueness of fixed points. WOS:000577160000001

The concept of Picard operator is one of the most important concept of fixed point theory. As known, a self mapping T of a metric space X is called Picard operator (PO) if it has unique fixed point and every Picard iteration sequence converges to this fixed point. There some weaker forms of PO in the litareture as weakly Picard operator (WPO) and pseudo Picard operator (PPO). In this study, we present a new kind of PO as almost Picard operator (APO) and we show the differences from the others. Then we show that every continuous P-contractive self mapping of a compact metric space is APO. Also we present some open problems.

In this paper, by using generalized viscosity mappings, we prove two strong convergence theorems for finding fixed points of a nonexpansive mapping which is also a unique solution of the variational inequality. Our results extend and improve the recent ones announced by some authors.

Altun, Ishak/0000-0002-7967-0554 WOS: 000454873800004 In the present paper, we introduce a new concept of P-contractive mappings on metric spaces. We prove that every ordinary contractive mapping is also P-contractive but the converse may not be true in general. We provide an example to illustrate this fact and also provide some examples to show that nonexpensive mappings and P-contractive mappings are independent on metric spaces. Finally, we present that every continuous P-contractive mapping on compact metric spaces has a unique fixed point. This result includes the famous Edelstein fixed point theorem.

By using the idea of Pata [V. Pata, A fixed point theorem in metric spaces. J. Fixed Point Theory Appl. 10 (2011) 299–305.] we establish a new common fixed point theorem and as an application, we prove the existence and uniqueness of common solutions for a class of system of functional equations arising in dynamic programming.

Resumen. En esta tesis se demostrará la existencia y unicidad de soluciones de una clase de ecuaciones integrales no lineales de tipo de Volterra definidas sobre espacios de Lebesgue con exponente variable. Para lograr este objetivo impondremos condiciones de crecimiento sobre los operadores asociados a estas ecuaciones, lo que nos permitirá usar técnicas de punto fijo para suma de aplicaciones de tipo contractivo, así como también el método de estimación a priori (grado topológico para aplicaciones α -condensantes). Abstract. This thesis is devoted to the study of existence and uniqueness of solutions for a class of non-linear Volterra integral equations definided on the so-called variable Lebesgue spaces. To attaing our goals, we will impose growth conditions on the associated operators, which allow us to use fixed point techniques for sum of contractive mapping, as well as the method of a priori bounds. Maestría

In this paper, in the framework of Lebesgue spaces with variable exponent, we are going to provide conditions for the existence and uniqueness of the solutions of a class of Volterra integral equations induced by Carath\'eodory functions having diverse growth behaviors. To attain our goals, we will use topological degree theory for condensing maps and fixed point results for the sum of mappings of contractive type.

In this paper, we introduce a concept of the c-distance in a cone metric space and, by using the concept of the c-distance, prove some fixed point theorems in ordered cone metric spaces.

In this paper, we prove some fixed point theorems in a b-metric-like space setting using a new class of admissible mappings and types of α − k and ( ψ , ϕ )-contractive conditions. Our results are supported by the application of finding solutions of integral equations and generalizing some well-known results of the literature.

In this paper, we prove the existence and uniqueness of solution for the fuzzy functional differential equation under generalized Hukuhara derivative via contractive-like mapping principles.

We develop the Hutchinson–Barnsley theory for finite families of mappings on a metric space endowed with a directed graph. In particular, our results subsume a classical theorem of J.E. Hutchinson [J.E. Hutchinson, Fractals and self-similarity, Indiana Univ. Math. J. 30 (1981) 713–747] on the existence of an invariant set for an iterated function system of Banach contractions, and a theorem of L. Mate [L. Mate, The Hutchinson–Barnsley theory for certain non-contraction mappings, Period. Math. Hungar. 27 (1993) 21–33] concerning finite families of locally uniformly contractions introduced by Edelstein. Also, they generalize recent fixed point theorems of A.C.M. Ran and M.C.B. Reurings [A.C.M. Ran, M.C.B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004) 1435–1443], J.J. Nieto and R. Rodriguez-Lopez [J.J. Nieto, R. Rodriguez-Lopez, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005) 223–239; J.J. Nieto, R. Rodriguez-Lopez, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.) 23 (2007) 2205–2212], and A. Petrusel and I.A. Rus [A. Petrusel, I.A. Rus, Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc. 134 (2006) 411–418] for contractive mappings on an ordered metric space. As an application, we obtain a theorem on the convergence of infinite products of linear operators on an arbitrary Banach space. This result yields new generalizations of the Kelisky–Rivlin theorem on iterates of the Bernstein operators on the space C [ 0 , 1 ] as well as its extensions given recently by H. Oruc and N. Tuncer [H. Oruc, N. Tuncer, On the convergence and iterates of q-Bernstein polynomials, J. Approx. Theory 117 (2002) 301–313], and H. Gonska and P. Piţul [H. Gonska, P. Piţul, Remarks on an article of J.P. King, Comment. Math. Univ. Carolin. 46 (2005) 645–652].

In this paper we introduce cone metric spaces, prove some fixed point theorems of contractive mappings on cone metric spaces.