The present paper aims to define three new notions: Θ e -contraction, a Hardy–Rogers-type Θ -contraction, and an interpolative Θ -contraction in the framework of extended b-metric space. Further, some fixed point results via these new notions and the study endeavors toward a feasible solution would be suggested for nonlinear Volterra–Fredholm integral equations of certain types, as well as a solution to a nonlinear fractional differential equation of the Caputo type by using the obtained results. It also considers a numerical example to indicate the effectiveness of this new technique.

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This paper, gives an answer for the Question 1.1 posed by Hitzler (Generalized metrics and topology in logic programming semantics, 2001) by means of "Topological aspects of d-metric space with d-neighborhood system". We have investigated the topological aspects of a d-neighborhood system obtained from dislocated metric space (simply d-metric space) which has got useful applications in the semantic analysis of logic programming. Further more we have generalized the notion of F-contraction in the view of d-metric spaces and investigated the uniqueness of fixed point and coincidence point of such mappings.

Dislocated metric space differs from metric space for a property that self distance of a point needs not to be equal to zero. This property plays an important role to deal with the problems of various disciplines to obtain fixed point results. In this article, we establish a common fixed point theorem for two pairs of weakly compatible mappings which generalize and extend the result of Brain Fisher [1] in the setting of dislocated metric space with replacement of contractive constant by contractive modulus for which continuity of mappings is not necessary and compatible mappings by weakly compatible mappings.

Dislocated symmetric spaces are introduced, and implications and nonimplications among various kinds of convergence axioms are derived.

Background: Student psychological health has been an increasing concern. The COVID-19 pandemic situation has brought this vulnerable population into renewed focus. Objective: Our study aims to conduct a timely assessment of the effects of the COVID-19 pandemic on the mental health of college graduates and postgraduates. Methodology: We conducted online survey with 550 students to understand the effects of the pandemic on their psychology and well-being. The data were analyzed through quantitative and qualitative methods. Results: Of the 550 students, 138 (71%) indicated increased stress and anxiety due to the COVID-19 outbreak. When asked about how the lockdown in COVID-19 situation affecting them, 97% said that it is severely affecting them. When asked about what the problems do you faced during online class, 5% said the Internet, 83.8% said noninteractive, and 11.2% said lack of explanatory mediums. When asked about number of hours spent on the Internet, 100% said more than 10 h. When asked about the activities to keep yourself busy during lockdown in COVID-19 situation, 37% said social media followed by 23% who mentioned cooking. Conclusion: Due to the long-lasting pandemic situation and onerous measures such as lockdown and stay-at-home orders, the COVID-19 pandemic brings negative impacts on education. The findings of our study highlight the urgent need to develop interventions and preventive strategies to address the psychological health of college students.

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