In this article, in the sequel of extending b-metric spaces, we modify controlled metric type spaces via two control functions α ( x , y ) and μ ( x , y ) on the right-hand side of the b - triangle inequality, that is, d ( x , y ) ≤ α ( x , z ) d ( x , z ) + μ ( z , y ) d ( z , y ) , for all x , y , z ∈ X . Some examples of a double controlled metric type space by two incomparable functions, which is not a controlled metric type by one of the given functions, are presented. We also provide some fixed point results involving Banach type, Kannan type and ϕ -nonlinear type contractions in the setting of double controlled metric type spaces.

https://www.mdpi.com/2227-7390/6/12/320/pdf

Double Controlled Metric Type Spaces and Some Fixed Point Results

In this paper we investigate some fixed-circle theorems using Ciric’s technique (resp. Hardy-Rogers’ technique, Reich’s technique and Chatterjea’s technique) on a metric space. To do this, we define new types of F c -contractions such as Ciric type, Hardy-Rogers type, Reich type and Chatterjea type. Two illustrative examples are presented to show the effectiveness of our results. Also, it is given an application of a Ciric type F c -contraction to discontinuous self-mappings which have fixed circles.

https://www.mdpi.com/2227-7390/6/10/188/pdf

New Types of Fc-Contractions and the Fixed-Circle Problem

In this paper, we define a Kuhn‐Tucker (KT)–pseudoinvex multidimensional control problem. More exactly, we introduce a new condition on the functions, which are involved in a multidimensional control problem, and we prove that a KT‐pseudoinvex multidimensional control problem is characterized such that a KT point is an optimal solution. Thus, we generalize optimality results in known mathematical programming problems. These theoretical results are illustrated with an application.

KT-pseudoinvex multidimensional control problem: KT-pseudoinvex multidimensional control problem

In this article, certain coupled fixed point theorems, which can be considered as generalizations of Banach fixed point theorem, are extended to bipolar metric spaces. Also, some results which are related to these theorems are obtained. Finally, it is given an example which presents to the applicability of obtained results.

Coupled Fixed Point Theorems on Bipolar Metric Spaces

In this article, we introduce some new class of preinvex functions involving two arbitrary auxiliary functions. We derive some new integral inequalities for these classes of preinvex functions. We also discuss some special cases which can be deduced from our main results.

https://www.mdpi.com/2227-7390/7/1/29/pdf

Some New Classes of Preinvex Functions and Inequalities

In this paper, we study some coupled fixed point results in a quasi-partial metric space. Also, we introduce some examples to support the useability of our results.

Some coupled fixed point theorems in quasi-partial metric spaces

In this work, we consider a new class of multitime multiobjective variational problems of minimizing a vector of functionals of curvilinear integral type. Based on the normal efficiency conditions for multitime multiobjective variational problems, we study duals of Mond-Weir type, generalized Mond-Weir-Zalmai type and under some assumptions of (?, b)-quasiinvexity, duality theorems are stated. We give weak duality theorems, proving that the value of the objective function of the primal cannot exceed the value of the dual. Moreover, we study the connection between values of the objective functions of the primal and dual programs, in direct and converse duality theorems. While the results in §1 and §2 are introductory in nature, to the best of our knowledge, the results in §3 are new and they have not been reported in literature.

Duality theorems for a new class of multitime multiobjective variational problems

In this paper we utilize the notion of Ω-distance in the sense of Saadati et al. (Math. Comput. Model. 52:797-801, 2010) to construct and prove some fixed and coupled fixed point theorems in a complete G-metric space for a nonlinear contraction. Also, we provide an example to support our results.

/pdf/fixed-and-coupled-fixed-point-theorems-of-omega-distance-for-3wq0rufn3d.pdf

Fixed and coupled fixed point theorems of omega-distance for nonlinear contraction

In this paper, we utilize the concept of (P)-property, weak (P)-property and the comparison function to introduce and prove an existence and uniqueness theorem of a best proximity point. Also, we introduce the notion of a best proximity coupled point of a mapping F : X X! X. Using this notion and the comparison function to prove an existence and uniqueness theorem of a best proximity coupled point. Our results extend and improve many existing results in the literature. Finally, we introduce examples to support our theorems.

/pdf/best-proximity-point-and-best-proximity-coupled-point-in-a-b8tlrom56p.pdf

Best Proximity Point and Best Proximity Coupled Point in a Complete Metric Space with (P)-Property

Strongly motivated by its possible applications in Mechanics, in our previous work (Pitea and Postolache (Optim. Lett. doi:10.1007/s11590-010-0272-0, 2011)), we initiated an optimization theory for the second order jet bundle. We considered the problem of minimization of vectors of curvilinear functionals (well known as mechanical work), thought as multi-time multi-objective variational problems, subject to PDE and/or PDI constraints. Within this framework, we introduced necessary conditions. As natural continuation of our results in Pitea and Postolache (Optim. Lett. doi:10.1007/s11590-010-0272-0, 2011), the present work introduces a study of sufficient efficiency conditions. While the background in Sect. 2 is introductory, the theory in Sect. 3 is new as a whole, containing our results.

Minimization of vectors of curvilinear functionals on the second order jet bundle: sufficient efficiency conditions

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