Our theorems are on ordered cone metric spaces which are not necessarily normal. In the end, we describe the application of the main results in the integral equation.Although Du in [W‎. ‎S‎. ‎Du‎, ‎A note on cone metric fixed point theory and its equivalence‎, ‎Nonlinear Analysis‎, ‎72(2010) 2259-2261.]‎, ‎showed that the fixed point results in the setting of cone...

In this paper, we give (?,?)-weak Pata contractive mapping by using the simulation function and multivalued contractions establish some fixed point results for such contractions. Also, an example related to mappings via function. Our generalize Pata-type Banach Consequently, obtained encompass several in literature.

In the present paper, we provide and verify several results obtained by using Chatterjea C`iric` fixed-point theorems (α−ψ)-contractive mapping in C*-algebra-valued metric space. We some examples an application to illustrate our results. Our study extends generalizes of studies literature.

and Applied Analysis 3 Lemma 7 (see [15]). LetC be a nonempty closed convex subset of a real Hilbert space H. Let T : C 󳨃→ C be a k-strict pseudo-contractive mapping. Let γ and δ be two nonnegative real numbers such that (γ + δ)k ≤ γ; then 󵄩󵄩󵄩γ (x − y) + δ (Tx − Ty) 󵄩󵄩󵄩 ≤ (γ + δ) 󵄩󵄩󵄩x − y 󵄩󵄩󵄩 , ∀x, y ∈ C. (21) Lemma 8 (see [16]). Let H be a Hilbert space and C a nonempty convex subset of H. Let...

We present a variational integration of nonlinear shape statistics into a Mumford–Shah based segmentation process. The nonlinear statistics are derived from a set of training silhouettes by a novel method of density estimation which can be considered as an extension of kernel PCA to a probabilistic framework. We assume that the training data forms a Gaussian distribution after a nonlinear mappi...

Abstract. We study a quasilinear parabolic Cauchy problem with a cumulative distribution function on the real line as an initial condition. We call ‘probabilistic solution’ a weak solution which remains a cumulative distribution function at all times. We prove the uniqueness of such a solution and we deduce the existence from a propagation of chaos result on a system of scalar diffusion process...

Support Vector Regression (SVR) solves regression problems based on the concept of Support Vector Machine (SVM). In this paper, a new model of SVR with probabilistic constraints is proposed that any of output data and bias are considered the random variables with uniform probability functions. Using the new proposed method, the optimal hyperplane regression can be obtained by solving a quadrati...