Transactions in Theoretical and Mathematical Physics

Transactions in Theoretical and Mathematical Physics

Quantitative Non-Unique Čirić Fixed-Point Theory under Residual-Sensitive C-Class Controls

Document Type : Original Article

Authors
Olaoluwa J Omidire 1
Memudu O Olatinwo 2
Kamiludeen R. Tijani 3
Babatunde T. Ishola 2
1 Department of Mathematical Sciences
2 Department of Mathematics, Obafemi Awolowo University, Ile Ife.
3 Department of Mathematical Sciences Osun State University Oke Baale
10.30511/ttmp.2026.2095466.1086
Abstract
Building on the non-unique fixed-point theory of Čirić and its known extensions by
c-comparison functions, we introduce a residual-sensitive three-variable C-class control that
acts as a verifiable certificate for summable decay of successive Picard displacements. The
main argument is organized around an orbital summability principle, which separates the
essential recurrence from the auxiliary contractive form. For an orbitally continuous self-map
on a T-orbitally complete metric space, the proposed condition makes the map weakly Picard
and yields both an a priori tail estimate and a genuine a posteriori estimate in terms of the
current residual d(Tnx,Tn+1x). These bounds induce an explicit retraction-displacement
modulus. As consequences, we obtain set-wise generalized Ulam stability, well-posedness
with respect to the fixed-point set, and a Hausdorff data-dependence estimate for the entire
set of fixed points under perturbations of the operator. A nonlinear example with two fixed
points exhibits non-geometric decay and cannot satisfy any corresponding constant-coefficient
inequality with q < 1. A second example shows that the linear Hausdorff perturbation bound
is sharp. The results place residual-sensitive C-class conditions within the quantitative theory
of weakly Picard operators without imposing uniqueness.
Keywords
Non-unique fixed point
Čirić mapping
weakly Picard operator
C-class control
Ulam stability
Subjects
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Transactions in Theoretical and Mathematical Physics
Volume 3, Issue 3
Summer 2026
Pages 104-112

  • Receive Date 24 July 2026
  • Accept Date 21 August 2026
  • First Publish Date 21 August 2026
  • Publish Date 01 August 2026