A discussion on generalized almost contractions via rational expressions in partially ordered metric spaces

The main purpose of this paper is to give some fixed point results for mappings involving generalized (Formula presented.)-contractions in partially ordered metric spaces. Our results generalize, extend, and unify several well-known comparable results in the literature (Jaggi in Indian J. Pure Appl. Math. 8(2):223-230, 1977, Harjani et al. in Nonlinear Anal. 71:3403-3410, 2009, Luong and Thuan in Fixed Point Theory Appl. 2011:46, 2011). The presented results are supported by three illustrative examples. MSC: 46N40, 47H10, 54H25, 46T99.Scopu

On common fixed points in G-metric spaces using (E.A) property

AbstractIn this paper, we introduce some new types of pairs of mappings (f,g) on G-metric spaces called G-weakly commuting of type Gf and G–R-weakly commuting of type Gf. We obtain also several common fixed point results by using the (E.A) property

Some remarks concerning D∗-metric spaces

In [S. Sedghi, N. Shobe, H. Y. Zhou, Fixed Point Theory Appl., 2007 (2007), 13 pages], Sedghi et al. introduced the notion of D∗ -metric space and in [S. Sedghi, N. Shobe, A. Aliouche, Mat. Vesnik, 64 (2012), 258–266] the authors claimed that every G-metric space is D∗ -metric. In this short paper we present examples to show that D∗ -metric need not be G-metric as well as the G-metric need not be D∗ -metric.Scopu

Tripled and coincidence fixed point theorems for contractive mappings satisfying Φ-maps in partially ordered metric spaces

Abstract In this paper, we study some tripled fixed and coincidence point theorems for two mappings F : X × X × X → X and g : X → X satisfying a nonlinear contraction based on φ-maps. Our results extend and improve many existing results in the literature. Also, we introduce an example to support the validity of our results

Existence of Fixed Point Results in -Metric Spaces

The purpose of this paper is to prove the existence of fixed points of contractive mapping defined on -metric space where the completeness is replaced with weaker conditions. Moreover, we showed that these conditions do not guarantee the completeness of -metric spaces

Fixed point results of F-rational cyclic contractive mappings on 0-complete partial metric spaces

© 2018 Forum-Editrice Universitaria Udinese SRL. All rights reserved. Wardowski [19] introduced a new concept of contraction which called F-contraction and proved a fixed point theorem on complete metric space. Following this direction of research, in this paper, we introduce an F-rational cyclic contraction on partial metric spaces and we present new fixed point results for such cyclic contraction in 0-complete partial metric spaces. An example is given to illustrate the main result, also an application to integral equation is given to show the usability of our results

Artificial intelligence (AI) based neural networks for a magnetized surface subject to tangent hyperbolic fluid flow with multiple slip boundary conditions

In this paper, the Levenberg-Marquardt backpropagation scheme is used to develop a neural network model for the examination of the fluid flow on a magnetized flat surface with slip boundaries. The tangent hyperbolic fluid is considered along with heat generation, velocity, and thermal slip effects at the surface. The problem is modelled in terms of a non-linear differential system and Lie symmetry is used to get the scaling group of transformation. The order reduction of differential equations is done by using Lie transformation. The reduced system is solved by the shooting method. The surface quantity, namely skin friction, is evaluated at the surface for the absence and presence of an externally applied magnetic field. A total of 88 sample values are estimated for developing an artificial neural network model to predict skin friction coefficient (SFC). Weissenberg number, magnetic field parameter, and power law index are considered three inputs in the first layer, while 10 neurons are taken in the hidden layer. 62 (70%), 13 (15%), and 13 (15%) samples are used for training, validation, and testing, respectively. The Levenberg-Marquardt backpropagation is used to train the network by entertaining the random 62 sample values. Both mean square error and regression analysis are used to check the performance of the developed neural networking model. The SFC is noticed to be high at a magnetized surface for power law index and Weissenberg number

C-class functions with new approach on coincidence point results for generalized (ψ,φ)-weakly contractions in ordered b-metric spaces

In this paper, by using the C-class functions and a new approach we present some coincidence point results for four mappings satisfying generalized (ψ,φ) -weakly contractive condition in the setting of ordered b-metric spaces. Also, an application and example are given to support our results.Scopu

Some fixed and periodic point results for generalized contractions on partial ordered metric space with applications in metric space

In this paper, we introduce new type of Θ-contraction in termof a self-mapping on a metric space to obtain common fixed point results. Some examples arealso provided to support the validity of our results and concepts presented herein.As an application of our results, periodic point results forthese Θ-contractions inmetric spaces are proved.Scopu

Extremal number of theta graphs of order 7

For a set of graphsF, letH(n;F) denote the class of non-bipartiteHamiltonian graphs onnvertices that does not contain any graph ofFas a subgraphandh(n;F) = max{E(G) :G∈H(n;F)}whereE(G) is the number of edges inG.In this paper we determineh(n;{θ4, θ5, θ7}) andh(n;θ7) for sufficiently odd largen. Our result confirms the conjecture made in [1] fork= 3.Scopu