On some novel results for C-weak-fuzzy contractions

This article implements the idea of introducing the concept of C-weak-fuzzy contraction mapping in the framework of fuzzy cone metric spaces, and deriving some unique common fixed point results. A nontrivial example is enunciated to uphold our results. Our results unify, enrich and extend some pioneer results in the existing literature in the fuzzy setting. In the end, an application to Fredholm nonlinear integral equation is offered showing the superiority of our results, which is in turn supported by an example.Publisher's Versio

Some critical remarks on “Some new fixed point results in rectangular metric spaces with an application to fractional-order functional differential equations”

In this manuscript, we generalize, improve, and enrich recent results established by Budhia et al. [L. Budhia, H. Aydi, A.H. Ansari, D. Gopal, Some new fixed point results in rectangular metric spaces with application to fractional-order functional differential equations, Nonlinear Anal. Model. Control, 25(4):580–597, 2020]. This paper aims to provide much simpler and shorter proofs of some results in rectangular metric spaces. According to one of our recent lemmas, we show that the given contractive condition yields Cauchyness of the corresponding Picard sequence. The obtained results improve well-known comparable results in the literature. Using our new approach, we prove that a Picard sequence is Cauchy in the framework of rectangular metric spaces. Our obtained results complement and enrich several methods in the existing state-ofart. Endorsing the materiality of the presented results, we also propound an application to dynamic programming associated with the multistage process

Convergence results based on graph-Reich contraction in fuzzy metric spaces with application

This article introduces a novel class of Reich-type contractions that meet the graph preservation criteria in the context of complete fuzzy metric spaces. The provided contraction condition is satisfied through various forms of contractive mappings via directed graphs in the literature. Our key result is the natural extension of fuzzy metric spaces to fuzzy metrics enriched with a graph, which adds the understanding of fixed points in metric spaces within the realm of graph structure. The findings are further supported by examples and applications

CONVERGENCE ANALYSIS FOR APPROXIMATING SOLUTION OF VARIATIONAL INCLUSION PROBLEM

This article aims to define a new resolvent operator for variational inclusion problems in the framework of  Banach spaces. We design a rapid algorithm using the resolvent operator to approximate the solution of the variational inclusion problem in Banach spaces. Additionally, we show that the algorithm articulated in this article converges faster than the well-known and notable algorithm due to Fang and Huang. To show the superiority and prevalence of the obtained results, we propound a numerical and computational example upholding our claim.  Lastly, a minimization problem is solved with the help of the proposed algorithm, which is the first attempt in the current context of the study

Clinicopathological profile and operative outcomes of gastric cancer patients in Kashmir: a high incidence area

Background: The objective of the present study was to analyse the demographic, clinicopathological and perioperative outcome of patients undergoing D2 gastrectomy in a high-volume tertiary care hospital in Kashmir a high incidence area.Methods: A total of 89 gastric cancer patients operated in the department of surgical gastroenterology, SKIMS, Kashmir, from January 2018 to December 2021 were included. A standardized D2 lymphadenectomy with spleen/pancreas preservation was performed.Results: Most of the patients in our study were elderly males and the mean age of patients in our series was 60.12±9.4. Majority of the patients in this study had stage III (91%) disease. Nodal involvement (N2, N3) was seen in 66% of patients. The average blood loss during operation was (380.23±48.53 ml) in our patients. The mean number of harvested lymph nodes was (26.6±10.1) with the range of (12-40). Mean operative time was (180±32.58 min). Average hospital stay was (8±2.46 days) in this series.Conclusions: Data from our study suggests that D2-gastrectomy when performed by skilled team in high volume centre like SKIMS is safe and should be the standard of care for gastric cancer for improved outcome. 

Some critical remarks on recent results concerning F−contractions in b-metric spaces

This paper aims to correct recent results on a generalized class of F−contractions in the context of b−metric spaces. The significant work consists of repairing some novel results involving F−contraction within the struc-ture of b-metric spaces. Our objective is to take advan-tage of the property (F 1) instead of the four properties viz. (F 1), (F 2), (F 3) and (F 4) applied in the results of Nazam et al. [“Coincidence and common fixed point theorems for four mappings satisfying (αs, F)−contraction", Nonlinear Anal: Model. Control., vol. 23, no. 5, pp. 664–690, 2018]. Our approach of proving the results uti-lizing only the condition (F 1) enriches, improves, and condenses the proofs of a multitude of results in the ex-isting state-of-art. © 2023 M. Younis et al

A study on the solutions of notable engineering models

In the commenced work, we establish some novel results concerning graph contractions in a more generalized setting. Furthermore, we deliver some examples to elaborate and explain the usability of the attained results. By virtue of nontrivial examples, we show our results improve, extend, generalize, and unify several noteworthy results in the existing state-of-art. We adopt computer simulation validating our results. To arouse further interest in the subject and to show its efficacy, we devote this work to recent applications which emphasize primarily the applications for the existence of the solution of various models related to engineering problems viz. fourth-order two-point boundary value problems describing deformations of an elastic beam, ascending motion of a rocket, and a class of integral equations. This approach is entirely new and will open up some new directions in the underlying graph structure

Bipolar <i>b</i>-Metric Spaces in Graph Setting and Related Fixed Points

In this article, we develop a new notion that combines fixed-point theory and graph theory: graphical bipolar b-metric spaces. We demonstrate fixed-point solutions in the framework of graphical bipolar b-metric spaces, employing covariant and contravariant mapping contractions, which is a new addition to this end. This article also features illustrative examples drawn from various contexts to further demonstrate our findings. This is a significant study since it melds ideas from graph theory with those from generalized bipolar metric spaces, and considers that the symmetry of the edges of the underlying graphs connected with the enunciated metric spaces is essential in the graphical metric spaces

Cerebrospinal fluid lactate: a differential biomarker for bacterial and viral meningitis in children

Objective: To assess the performance of cerebrospinal fluid (CSF) lactate as a biomarker to differentiate bacterial meningitis (BM) from viral meningitis (VM) in children, and to define an optimal CSF lactate concentration that can be called significant for the differentiation. Methods: Children with clinical findings compatible with meningitis were studied. CSF lactate and other conventional CSF parameters were recorded. Results: At a cut‐off value of 3 mmol/L, CSF lactate had a sensitivity of 0.90, specificity of 1.0, positive predictive value of 1.0, and negative predictive value of 0.963, with an accuracy of 0.972. The positive and negative likelihood ratios were 23.6 and 0.1, respectively. When comparing between BM and VM, the area under the curve (AUC) for CSF lactate was 0.979. Conclusions: The authors concluded that CSF lactate has high sensitivity and specificity in differentiating bacterial from viral meningitis. While at a cut‐off value of 3 mmol/L, CSF lactate has high diagnostic accuracy for BM, mean levels in VM remain essentially below 2 mmol/L

Cerebrospinal fluid lactate: a differential biomarker for bacterial and viral meningitis in children

Abstract Objective: To assess the performance of cerebrospinal fluid (CSF) lactate as a biomarker to differentiate bacterial meningitis from viral meningitis in children, and to define an optimal CSF lactate concentration that can be called significant for the differentiation. Methods: Children with clinical findings compatible with meningitis were studied. CSF lactate and other conventional CSF parameters were recorded. Results: At a cut-off value of 3 mmol/L, CSF lactate had a sensitivity of 0.90, specificity of 1.0, positive predictive value of 1.0, and negative predictive value of 0.963, with an accuracy of 0.972. The positive and negative likelihood ratios were 23.6 and 0.1, respectively. When comparing between bacterial and viral meningitis, the area under the curve for CSF lactate was 0.979. Conclusions: The authors concluded that CSF lactate has high sensitivity and specificity in differentiating bacterial from viral meningitis. While at a cut-off value of 3 mmol/L, CSF lactate has high diagnostic accuracy for bacterial meningitis, mean levels in viral meningitis remain essentially below 2 mmol/L